Hydrodynamic torque converters, also called converters for short in what follows, are used as starting aids in automatic transmissions for motor vehicles. To improve the efficiency of the automatic transmission the converter is equipped with a converter bridging clutch, called a converter clutch for short in what follows. Known converter clutches comprise a clutch piston, which is acted upon by a hydraulic liquid, referred to as oil in what follows, and thereby forms a torque connection between a pump wheel and a turbine wheel. The converter is thus bridged. The oil is supplied to the converter or converter clutch by two lines coming from a hydraulic switching unit which, as a rule, is arranged under the automatic change-speed transmission. The hydraulic switching unit (abbreviated to HSU) comprises a plurality of valves and valve slides which, among other things, also control the flow of oil to and from the converter. When the converter is active the converter clutch is disengaged. The oil then flows from the hydraulic switching unit through a line to the converter past the front side of the converter piston and, on its rear side, flows back again through another line to the hydraulic switching unit. From there the oil flows into an oil cooler. When the converter clutch is to be engaged, the flow direction in the two lines is reversed by the hydraulic switching unit so that the rear side of the converter piston is acted upon by an engagement force and the converter is thereby bridged. The disadvantage of this known oil flow system is that the return flow of the oil when the converter clutch is disengaged takes place via the hydraulic switching unit or the corresponding control valve, and this causes a pressure loss which reduces the oil flow through the converter.